Using recent knowledge in data stream clustering we present a modified approach to the facility location problem in the context of geometric data streams. We give insight to the existing algorithm from a less mathematical point of view, focusing on understanding and practical use, namely by computer graphics experts. We propose a modification of the original data stream k-median clustering to s...

An evaluation of spatial patterns and a clustering play an important role among methods of spatial statistics. However, traditional clustering techniques are seldom suitable for analyses of spatial data and patterns because they usually do not count on spatial relations and qualities of objects. This paper aims to introduce usage of methods of spatial clustering estimation, which are based main...

In this work, the capacitated location-routing problem with simultaneous pickup and delivery (CLRP-SPD) is considered. This problem is a more realistic case of the capacitated location-routing problem (CLRP) and belongs to the reverse logistics of the supply chain. The problem has many real-life applications of which some have been addressed in the literature such as management of liquid petrol...

Facility location-network design (FLND) problem, which determines the location of facilities and also communication links between the demand and facility nodes, is arisen from the combination of the facility location and network design problems. This paper deals with fuzzy capacitated facility location-network design model which aims to select the facilities and candidate links in a way that yi...

The k-median problem is a variant of the uncapacitated facility location problem that we covered last week, with the difference that instead of a cost for each facility, we have a bound k on the number of facilities. Here is the definition of k-median problem: Problem 1. Given a set of locations(clients) V , a set F̃ of facilities, a cost function between two locations C : (V ⋃ F̃ ) ∗ (V ⋃ F̃ ) → ...

Microaggregation is a cardinality-constrained clustering problem that arose in the context of data privacy. In microaggregation, the number of clusters is not fixed beforehand, but each cluster must have at least k elements. We illustrate in this paper that microaggregation can be applied for decision making in areas other than privacy. Specifically, we focus on the service facility location pr...

We generalize the k-means algorithm presented by the authors [14] and show that the resulting algorithm can solve a larger class of clustering problems that satisfy certain properties (existence of a random sampling procedure and tightness). We prove these properties for the k-median and the discrete k-means clustering problems, resulting in O(2 O(1) dn) time (1 + ε)-approximation algorithms fo...

This paper explores three concepts: the k-center problem, some of its variants, and asymmetry. The k-center problem is a fundamental clustering problem, similar to the k-median problem. Variants of k-center may more accurately model real-life problems than the original formulation. Asymmetry is a significant impediment to approximation in many graph problems, such as k-center, facility location...

We present approximation algorithms for the metric uncapacitated facility location problem and the metric k-median problem achieving guarantees of 3 and 6 respectively. The distinguishing feature of our algorithms is their low running time: O(m log m) and O(m logm(L+log(n))) respectively, where n and m are the total number of vertices and edges in the underlying graph. The main algorithmic idea...

Determination of facilities, such as factories or warehouses, location and availability conditions is one of the important and strategic decisions for an organization to make. Transportation costs that form a major part of goods price are dependent to this decision making. There are verity of methods have been presented to achieve the optimal locations of these facilities which are generally de...